Mathematical fictionalism vs. physical fictionalism

[Dennis E. Hamilton]

> From: FOM <fom-bounces at cs.nyu.edu> On Behalf Of Vaughan Pratt

> Whereas Bohmian mechanics maintains that particles such as electrons move 
> continuously, the Copenhagen Interpretation maintains that electrons in 
> orbitals only exist as distributions and not as actual continuously moving 
> particles.

> These being contradictory points of view, must we infer that at least one of 
> them is fictional?

I favor the Einstein view that they are all fictional.  There are two places 
where he asserted the difference between physics as (mathematical) theories 
and the contingent reality.

First, with regard to the uncanny applicability of mathematics to physics, he 
illustrated his thinking by contrasting axiomatics (e.g., for geometry) and 
intended interpretations with respect to physics.  My appraisal is at
 <https://orcmid.com/blog/2010/02/abstraction-einstein-on-theoryreality.asp>.

Another account is a serious statement in the 1938 book with Infield:

"Physical concepts are free creations of the human mind, and are not, however 
they may seem, uniquely determined by the external world.  In our endeavor to 
understand reality we are somewhat like a man trying to understand the 
mechanism of a closed watch. ... If he is ingenious he may form some picture 
of a mechanism which could be responsible for all the things he observes, but 
he may never be quite sure is picture is the only one which could explain his 
observations.  He will never be able to compare his picture with the real 
mechanism and he cannot even imagine the possibility or meaning of such a 
comparison."   p. 31 in [Einstein, Albert., Infeld, Leopold.  The Evolution of 
Physics.  Touchstone (New York: 1938), ISBN 0-671-20156-5.]